A metallic spherical shell has an inner radius R_1 and outer radi… - Vidyadip

MCQ

A metallic spherical shell has an inner radius $R_1$ and outer radius $R_2$. A charge $Q$ is placed at the centre of the spherical cavity. What will be surface charge density on the inner surface

A
$\frac{Q}{{4\pi R_1^2}}$
✓
$ - \frac{Q}{{4\pi R_1^2}}$
C
$\frac{Q}{{4\pi R_2^2}}$
D
$ - \frac{Q}{{4\pi R_2^2}}$

✓

Answer

Correct option: B.

$ - \frac{Q}{{4\pi R_1^2}}$

b
A charge $\mathrm{Q}$ is placed at the centre of the spherical cavity. So, the charge induced at the inner surface of the sphere will be -Q and at outer surface of the sphere is $+Q$.

The surface charge density on the inner surface $\sigma_{1}=\frac{\text { Charge }}{\text { Area }}=\frac{-Q}{4 \pi R_{1}^{2}}$

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